
where \(d_H( \Theta ) = \max \lbrace \max _{k\in  \min _{\theta \in \Theta } |k- \theta |,\max _{\theta \in \Theta } \min _{k\in  |\theta - k|\rbrace denotes the Hausdorff distance.}}\section {Review of data segmentation methodologies}\) Broadly, algorithms for the canonical segmentation problem can be categorised into two:
One line of research casts the problem as that of globally optimising an objective function,
which imposes a penalty on the model complexity given e.g. by the number of change points;
the other is closely related to the change point testing literature,
whereby the test for detecting a single change point is applied locally
for detection and estimation of multiple change points.
We briefly mention that there exist methods based on hidden Markov models
where the main focus lies in modelling such phenomena,
with algorithms for estimating the sequence of hidden states [1]}, [2]}.
There are also methods allowing for Bayesian inference under change point models
[3]}, [4]}, [5]}, [6]}, [7]},
see [8]} for further references.
